Problem: Simplify the following expression: $q = \dfrac{-10t^2 + 100t - 160}{t - 8} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-10$ , so we can rewrite the expression: $ q =\dfrac{-10(t^2 - 10t + 16)}{t - 8} $ Then we factor the remaining polynomial: $t^2 {-10}t + {16} $ ${-8} {-2} = {-10}$ ${-8} \times {-2} = {16}$ $ (t {-8}) (t {-2}) $ This gives us a factored expression: $\dfrac{-10(t {-8}) (t {-2})}{t - 8}$ We can divide the numerator and denominator by $(t + 8)$ on condition that $t \neq 8$ Therefore $q = -10(t - 2); t \neq 8$